Afterward, the girls told the media the Queen was not in on the plot -- explaining they had tried to catch her in the background of a selfie ... and when Her Majesty realized what was going on, she hammed it up and flashed some pearly whites for the pic.

The girls say the Queen then approached them to talk sports -- "She asked us a bit about the pitch, how we were going and told us to enjoy our time here. She was lovely. Really, really lovely."